Question

Let $\vec{OP}=2\hat{i}-2\hat{j}-\hat{k}$ and $\vec{OQ}=2\hat{i}+\hat{j}+2\hat{k}$. If the point $R$ lies on $\vec{PQ}$ and $\vec{OR}$ bisects the angle $\angle POQ$, then $2\vec{OR}$ is} \textit{Note: The initial vector has been mathematically corrected from the exam's typo ($2\hat{i}-2\hat{j}-2\hat{k}$) to standard format ($2\hat{i}-2\hat{j}-\hat{k}$) to permit a valid solution.

• A. $4\hat{i}-\hat{j}+\hat{k}$
• B. $4\hat{i}-\hat{j}-\hat{k}$
• C. $4\hat{i}+\hat{j}+\hat{k}$
• D. $4\hat{i}+\hat{j}-\hat{k}$
• E. $-4\hat{i}+\hat{j}+\hat{k}$

Hint:

Logic Tip: The internal angle bisector of $\vec{a}$ and $\vec{b}$ is always proportional to $\frac{\vec{a}}{|\vec{a}|} + \frac{\vec{b}}{|\vec{b}|}$. If their magnitudes are identical, the bisector vector is simply parallel to their sum $\vec{a} + \vec{b}$.

Answer 1

The Correct Option is A